PA $13-1($Static$)$ Dan McClure owns a thriving independent bookstore..

Dan McClure owns a thriving independent bookstore in artsy New Hope, Pennsylvania. He must decide how many copies to order of a new book, Power and Self$-$Destruction, an expos$$ on a famous politician's lurid affairs. Interest in the book will be intense at first and then fizzle quickly as attention turns to other celebrities. The book's retail price is $$20,$ and the wholesale price is $$12.$ The publisher will buy back the retailer's leftover copies at a full refund, but McClure Books incurs $$4$ in shipping and handling costs for each book returned to the publisher. Dan believes his demand forecast can be represented by a normal distribution with a mean of $200$ and a standard deviation of $80.$ Use Table $13\mathrm{.}4.$

If a part of the question specifies whether to use Table $13\mathrm{.}4,$ or to use Excel, then credit for a correct answer will depend on using the specified method.

Dan will consider this book to be a blockbuster for him if it sells more than $400$

a$.$ units. What is the probability that Power and Self$-$Destruction will be a blockbuster?

$($Round your answer to $4$ decimal places.$)$

b$.$ Dan considers a book a "dog" if it sells less than $50$ percent of his mean forecast. What is the probability this expose is a "dog"? Use Excel.

$($Round your answer to $4$ decimal places.$)$

c$.$ What is the probability that demand for this book will be within $20$ percent of the mean forecast?

d$.$ What order quantity maximizes Dan's expected profit?

$($Round your answer to $2$ decimal places.$)$

If Dan orders the quantity needed to achieve a $95$ percent in$-$stock probability,

e$.$ what is the probability that some customer won't be able to purchase a copy of the book?

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$5$ of $12$

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